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Coulomb’s law for electrostatic force between two point charges and Newton’s law for gravitational force between two stationary point masses, both have inverse-square dependence on the distance between the charges/masses. (a) Compare the strength of these forces by determining the ratio of their magnitudes (i) for an electron and a proton and (ii) for two protons. (b) Estimate the accelerations of electron and proton due to the electrical force of their mutual attraction when they are 1A(=1010m)apart?(mp=1.67×1027kg,me=9.11×1031kg).

Answer
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Hint: Concept of natural gravitational force and electric force. By finding the ratio of the forces in different cases, the strengths can be compared easily.According to Coulomb’s law, the force of attraction or repulsion between two charged bodies is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. It acts along the line joining the two charges considered to be point charges.

Formula used:
1. Gravitational force
Fg=Gm1m2r2
Where m1andm2 are masses of two bodies separated by a distance r.
G is the gravitational constant.
2. Electrostatic force
Fe=Kq1q2r2
Where q1andq2 are masses of two bodies separated by a distance r.
K is a constant.

Complete step by step solution:
Gravitational Force – According to universal law of gravitation each and every object in this universe attracts another object with a force given by
Fg=Gm1m2r2
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Where m1andm2 are two particles separated by a distance of r.
- It follows inverse square law
- Gravitational force is always attractive in nature
- G is the universal gravitational constant and G=6.67×1011Nm2/Kg2
- Coulomb’s law: According to Coulomb’s s law, two charge particles of charges q1andq2 and separated by a distance r exerts an electrostatic force on each other given by
Fe=Kq1q2r2
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where k is a constant.
- The value of k is
K=14πε0=9×109Nm2/C2
- It can be attractive or repulsive
- For similar charges, it is repulsive
- For opposite charges, it is attractive in nature.

(a) (i) Ratio of Coulomb force to gravitational force for an electron and a proton Here,
q1=e=1.6×1019cq2=p=1.6×1019c
Mass of electron (m1)=9.1×1031kg
Mass of proton (m2)=1.67×1027kg
Required ratio (r1)=FeFg=Kq1q2r2Gm1m2r2
r1=K×q1×q2G×m1×m2
=9×109×(1.6×1019)×(1.6×1019)6.67×1011×9.1×1031×1.67×1027
=2.27×10391
(ii) Ratio of Coulomb force to gravitational force of two protons is
r2=K×q1×q2r2G×m1×m2r2
Here,
q1=q2=p=1.6×1019C
Mass of proton m1=m2=1.67×1027kg
So, r2=Kq12Gm12
r2=9×109×(1.6×1019)6.67×1011×(1.67×1027)2
=1.24×10361
(b) Coulomb force between electron and proton is given by
F=Kq1q2r2
Here
q1=e=1.6×1019c
q2=p=1.6×1019c
r=1A=1010m
So,
F=9×109×(1.6×1019)×(1.6×1019)×(1.6×1019)(1010)2
 F=2.304×108N
Now, according to Newton’s second law, F=maa=F/m.
So, acceleration of electron will be
a1=Fm1 Where m= mass of electron (m1=9.1×1031kg)
a1=2.304×1089.1×1031
a1=2.5×1022m/s2
The acceleration for proton is given by
a2=Fm2
Where m2= mass of proton, (m2=1.67×1027kg)
So,
a2=2.304×1081.67×1027
a2=1.4×1019m/s2.

Note:
Remember although charges on both electron and proton are equal but they are equal only in magnitude but opposite in their polarity. Also proton is heavier than that of electrons although both have the same charges.Moreover,a French physicist Charles Augustin de Coulomb in 1785 coined a tangible relationship in mathematical form between two bodies that have been electrically charged. He published an equation for the force causing the bodies to attract or repel each other which is known as Coulomb’s law or Coulomb’s inverse-square law.
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